<!DOCTYPE html>



  


<html class="theme-next muse use-motion" lang="zh-Hans">
<head>
  <meta charset="UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1"/>
<meta name="theme-color" content="#222">









<meta http-equiv="Cache-Control" content="no-transform" />
<meta http-equiv="Cache-Control" content="no-siteapp" />
















  
  
  <link href="/blog/lib/fancybox/source/jquery.fancybox.css?v=2.1.5" rel="stylesheet" type="text/css" />







<link href="/blog/lib/font-awesome/css/font-awesome.min.css?v=4.6.2" rel="stylesheet" type="text/css" />

<link href="/blog/css/main.css?v=5.1.4" rel="stylesheet" type="text/css" />


  <link rel="apple-touch-icon" sizes="180x180" href="/blog/images/apple-touch-icon-next.png?v=5.1.4">


  <link rel="icon" type="image/png" sizes="32x32" href="/blog/images/favicon-32x32-next.png?v=5.1.4">


  <link rel="icon" type="image/png" sizes="16x16" href="/blog/images/favicon-16x16-next.png?v=5.1.4">


  <link rel="mask-icon" href="/blog/images/logo.svg?v=5.1.4" color="#222">





  <meta name="keywords" content="算法,回溯法,数字组合," />










<meta name="description" content="数字组合等式问题疑难问题汇总： 1 2 3 4 5 6 7 8 9 &#x3D; 110这个题和上面那个题的递归差不多只不过是设置三种符号+，-，’ ’,遇到第一个就执行加，遇到第二个就减去，遇到第三个就合并，唯一不同就是你不能立马相加或者相减，而要把这个操作传入到下一个状态再决定  不理解传入下一个状态再做决定。。。我这个直接相加减了，但是遇到’ ’的时候好像处理的太复杂不对 12345678910111">
<meta property="og:type" content="article">
<meta property="og:title" content="数字排列组合问题">
<meta property="og:url" content="http://yangshucheng2020.gitee.io/blog/2020/03/27/%E6%95%B0%E5%AD%97%E7%BB%84%E5%90%88%E7%AD%89%E5%BC%8F%E9%97%AE%E9%A2%98/index.html">
<meta property="og:site_name" content="羊书">
<meta property="og:description" content="数字组合等式问题疑难问题汇总： 1 2 3 4 5 6 7 8 9 &#x3D; 110这个题和上面那个题的递归差不多只不过是设置三种符号+，-，’ ’,遇到第一个就执行加，遇到第二个就减去，遇到第三个就合并，唯一不同就是你不能立马相加或者相减，而要把这个操作传入到下一个状态再决定  不理解传入下一个状态再做决定。。。我这个直接相加减了，但是遇到’ ’的时候好像处理的太复杂不对 12345678910111">
<meta property="og:image" content="http://yangshucheng2020.gitee.io/Users/yangshucheng/Library/Application%20Support/typora-user-images/image-20200310151923689.png">
<meta property="article:published_time" content="2020-03-27T02:58:32.850Z">
<meta property="article:modified_time" content="2020-03-27T04:34:38.121Z">
<meta property="article:author" content="羊书">
<meta property="article:tag" content="算法">
<meta property="article:tag" content="回溯法">
<meta property="article:tag" content="数字组合">
<meta name="twitter:card" content="summary">
<meta name="twitter:image" content="http://yangshucheng2020.gitee.io/Users/yangshucheng/Library/Application%20Support/typora-user-images/image-20200310151923689.png">



<script type="text/javascript" id="hexo.configurations">
  var NexT = window.NexT || {};
  var CONFIG = {
    root: '/blog/',
    scheme: 'Muse',
    version: '5.1.4',
    sidebar: {"position":"left","display":"post","offset":12,"b2t":false,"scrollpercent":false,"onmobile":false},
    fancybox: true,
    tabs: true,
    motion: {"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"slideDownIn","post_body":"slideDownIn","coll_header":"slideLeftIn","sidebar":"slideUpIn"}},
    duoshuo: {
      userId: '0',
      author: '博主'
    },
    algolia: {
      applicationID: '',
      apiKey: '',
      indexName: '',
      hits: {"per_page":10},
      labels: {"input_placeholder":"Search for Posts","hits_empty":"We didn't find any results for the search: ${query}","hits_stats":"${hits} results found in ${time} ms"}
    }
  };
</script>



  <link rel="canonical" href="http://yangshucheng2020.gitee.io/blog/2020/03/27/数字组合等式问题/"/>





  <title>数字排列组合问题 | 羊书</title>
  








<meta name="generator" content="Hexo 4.2.0"></head>

<body itemscope itemtype="http://schema.org/WebPage" lang="zh-Hans">

  
  
    
  

  <div class="container sidebar-position-left page-post-detail">
    <div class="headband"></div>

    <header id="header" class="header" itemscope itemtype="http://schema.org/WPHeader">
      <div class="header-inner"><div class="site-brand-wrapper">
  <div class="site-meta ">
    

    <div class="custom-logo-site-title">
      <a href="/blog/"  class="brand" rel="start">
        <span class="logo-line-before"><i></i></span>
        <span class="site-title">羊书</span>
        <span class="logo-line-after"><i></i></span>
      </a>
    </div>
      
        <p class="site-subtitle"></p>
      
  </div>

  <div class="site-nav-toggle">
    <button>
      <span class="btn-bar"></span>
      <span class="btn-bar"></span>
      <span class="btn-bar"></span>
    </button>
  </div>
</div>

<nav class="site-nav">
  

  
    <ul id="menu" class="menu">
      
        
        <li class="menu-item menu-item-home">
          <a href="/blog/" rel="section">
            
              <i class="menu-item-icon fa fa-fw fa-home"></i> <br />
            
            首页
          </a>
        </li>
      
        
        <li class="menu-item menu-item-tags">
          <a href="/blog/tags/" rel="section">
            
              <i class="menu-item-icon fa fa-fw fa-tags"></i> <br />
            
            标签
          </a>
        </li>
      
        
        <li class="menu-item menu-item-categories">
          <a href="/blog/categories/" rel="section">
            
              <i class="menu-item-icon fa fa-fw fa-th"></i> <br />
            
            分类
          </a>
        </li>
      
        
        <li class="menu-item menu-item-archives">
          <a href="/blog/archives/" rel="section">
            
              <i class="menu-item-icon fa fa-fw fa-archive"></i> <br />
            
            归档
          </a>
        </li>
      

      
    </ul>
  

  
</nav>



 </div>
    </header>

    <main id="main" class="main">
      <div class="main-inner">
        <div class="content-wrap">
          <div id="content" class="content">
            

  <div id="posts" class="posts-expand">
    

  

  
  
  

  <article class="post post-type-normal" itemscope itemtype="http://schema.org/Article">
  
  
  
  <div class="post-block">
    <link itemprop="mainEntityOfPage" href="http://yangshucheng2020.gitee.io/blog/blog/2020/03/27/%E6%95%B0%E5%AD%97%E7%BB%84%E5%90%88%E7%AD%89%E5%BC%8F%E9%97%AE%E9%A2%98/">

    <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
      <meta itemprop="name" content="羊书">
      <meta itemprop="description" content="">
      <meta itemprop="image" content="/blog/images/avatar.gif">
    </span>

    <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
      <meta itemprop="name" content="羊书">
    </span>

    
      <header class="post-header">

        
        
          <h1 class="post-title" itemprop="name headline">数字排列组合问题</h1>
        

        <div class="post-meta">
          <span class="post-time">
            
              <span class="post-meta-item-icon">
                <i class="fa fa-calendar-o"></i>
              </span>
              
                <span class="post-meta-item-text">发表于</span>
              
              <time title="创建于" itemprop="dateCreated datePublished" datetime="2020-03-27T10:58:32+08:00">
                2020-03-27
              </time>
            

            

            
          </span>

          
            <span class="post-category" >
            
              <span class="post-meta-divider">|</span>
            
              <span class="post-meta-item-icon">
                <i class="fa fa-folder-o"></i>
              </span>
              
                <span class="post-meta-item-text">分类于</span>
              
              
                <span itemprop="about" itemscope itemtype="http://schema.org/Thing">
                  <a href="/blog/categories/%E5%AD%A6%E4%B9%A0/" itemprop="url" rel="index">
                    <span itemprop="name">学习</span>
                  </a>
                </span>

                
                
              
            </span>
          

          
            
          

          
          

          

          

          

        </div>
      </header>
    

    
    
    
    <div class="post-body" itemprop="articleBody">

      
      

      
        <h1 id="数字组合等式问题"><a href="#数字组合等式问题" class="headerlink" title="数字组合等式问题"></a>数字组合等式问题</h1><p>疑难问题汇总：</p>
<h2 id="1-2-3-4-5-6-7-8-9-110"><a href="#1-2-3-4-5-6-7-8-9-110" class="headerlink" title="1 2 3 4 5 6 7 8 9 = 110"></a>1 2 3 4 5 6 7 8 9 = 110</h2><p>这个题和上面那个题的递归差不多只不过是设置三种符号+，-，’ ’,遇到第一个就执行加，遇到第二个就减去，遇到第三个就合并，唯一不同就是你不能立马相加或者相减，而要把这个操作传入到下一个状态再决定</p>
<p><img src="/Users/yangshucheng/Library/Application%20Support/typora-user-images/image-20200310151923689.png" alt="image-20200310151923689"></p>
<p>不理解传入下一个状态再做决定。。。我这个直接相加减了，但是遇到’ ’的时候好像处理的太复杂不对</p>
<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;vector&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;iostream&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="meta-keyword">include</span> <span class="meta-string">&lt;string&gt;</span></span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> <span class="built_in">std</span>;</span><br><span class="line"><span class="keyword">const</span> <span class="keyword">int</span> N = <span class="number">3</span>;</span><br><span class="line"><span class="keyword">int</span> a[<span class="number">9</span>] = &#123; <span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>,<span class="number">4</span>,<span class="number">5</span>,<span class="number">6</span>,<span class="number">7</span>,<span class="number">8</span>,<span class="number">9</span> &#125;;<span class="comment">//将数字间的空格看做符号，扫描到空格则合并，扫描到符号则计算，共有3^8种数字组合形式</span></span><br><span class="line"><span class="keyword">char</span> c[N] = &#123; <span class="string">'+'</span>,<span class="string">'-'</span>,<span class="string">' '</span> &#125;;</span><br><span class="line"><span class="keyword">int</span> ans = <span class="number">110</span>;</span><br><span class="line"><span class="built_in">vector</span>&lt;<span class="keyword">char</span>&gt; equs;</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">joint</span><span class="params">(<span class="keyword">int</span> old,<span class="keyword">int</span> right)</span></span>&#123;<span class="comment">//拼接old与right</span></span><br><span class="line">    <span class="keyword">int</span> newnum = old*<span class="number">10</span> + right;</span><br><span class="line">    <span class="keyword">return</span> newnum;</span><br><span class="line">&#125;</span><br><span class="line"><span class="comment">//枚举所有的符号</span></span><br><span class="line"><span class="function"><span class="keyword">void</span> <span class="title">cal</span><span class="params">(<span class="keyword">int</span> k, <span class="keyword">int</span> len)</span> </span>&#123;<span class="comment">//k为当前扫描的数字的位数，len为数组中间的可填充符号个数</span></span><br><span class="line">    <span class="keyword">if</span> (k &gt;= len) &#123;</span><br><span class="line">        <span class="keyword">int</span> i = <span class="number">0</span>, j = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">int</span> left = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">int</span> right;</span><br><span class="line">        <span class="keyword">char</span> op = <span class="string">'+'</span>;</span><br><span class="line">        <span class="keyword">while</span> (i &lt;= equs.<span class="built_in">size</span>()) &#123;</span><br><span class="line">            <span class="keyword">while</span> (i &lt; equs.<span class="built_in">size</span>() &amp;&amp; equs[i] == <span class="string">' '</span>)i++;</span><br><span class="line">            right = a[j];</span><br><span class="line">            <span class="keyword">while</span> (j &lt; i) &#123;</span><br><span class="line">                right = joint(right, a[j + <span class="number">1</span>]);</span><br><span class="line">                j++;</span><br><span class="line">            &#125;</span><br><span class="line">            <span class="keyword">if</span> (op == <span class="string">'+'</span>)&#123;</span><br><span class="line">                left += right;</span><br><span class="line">            &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">                left -= right;</span><br><span class="line">            &#125;</span><br><span class="line">                op = equs[i++];</span><br><span class="line">                j = i;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">if</span> (left == ans) &#123;</span><br><span class="line">            <span class="built_in">cout</span>&lt;&lt;<span class="number">1</span>;</span><br><span class="line">            <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; equs.<span class="built_in">size</span>(); i++) &#123;</span><br><span class="line">                <span class="keyword">if</span> (equs[i]!=<span class="string">' '</span>) &#123;</span><br><span class="line">                    <span class="built_in">cout</span> &lt;&lt; <span class="string">" "</span> &lt;&lt; equs[i] &lt;&lt; <span class="string">" "</span>;</span><br><span class="line">                &#125;</span><br><span class="line">                    <span class="built_in">cout</span> &lt;&lt; a[i+<span class="number">1</span>];</span><br><span class="line">            &#125;</span><br><span class="line">            <span class="built_in">cout</span> &lt;&lt; <span class="string">" = "</span> &lt;&lt; ans &lt;&lt; <span class="built_in">endl</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; N; i++) &#123;<span class="comment">//先对各种符号进行枚举，全部压入equs里，对字符进行选择，先往符号数组加入，再递归调用</span></span><br><span class="line">        <span class="keyword">char</span> op = c[i];</span><br><span class="line">        <span class="keyword">if</span> (op == <span class="string">'+'</span>) &#123;</span><br><span class="line">            equs.push_back(<span class="string">'+'</span>);</span><br><span class="line">            cal(k + <span class="number">1</span>, len);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == <span class="string">'-'</span>) &#123;</span><br><span class="line">            equs.push_back(<span class="string">'-'</span>);</span><br><span class="line">            cal(k + <span class="number">1</span>, len);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">else</span> <span class="keyword">if</span> (op == <span class="string">' '</span>) &#123;<span class="comment">//遇到空格，合并前一个（可能已经拼接的）数字与后一个数字两个数字</span></span><br><span class="line">            equs.push_back(<span class="string">' '</span>);</span><br><span class="line">            cal(k + <span class="number">1</span>, len);</span><br><span class="line">        &#125;</span><br><span class="line">        equs.pop_back();<span class="comment">//都试过却不可以得出正确结果则把符号弹出</span></span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">int</span> <span class="title">main</span><span class="params">()</span> </span>&#123;</span><br><span class="line">    cal(<span class="number">0</span>, <span class="number">8</span>);</span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>





      
    </div>
    
    
    

    

    

    

    <footer class="post-footer">
      
        <div class="post-tags">
          
            <a href="/blog/tags/%E7%AE%97%E6%B3%95/" rel="tag"># 算法</a>
          
            <a href="/blog/tags/%E5%9B%9E%E6%BA%AF%E6%B3%95/" rel="tag"># 回溯法</a>
          
            <a href="/blog/tags/%E6%95%B0%E5%AD%97%E7%BB%84%E5%90%88/" rel="tag"># 数字组合</a>
          
        </div>
      

      
      
      

      
        <div class="post-nav">
          <div class="post-nav-next post-nav-item">
            
              <a href="/blog/2020/03/27/%E5%9B%9E%E6%BA%AF%E6%B3%95/" rel="next" title="回溯法">
                <i class="fa fa-chevron-left"></i> 回溯法
              </a>
            
          </div>

          <span class="post-nav-divider"></span>

          <div class="post-nav-prev post-nav-item">
            
              <a href="/blog/2020/03/27/%E6%B1%82%E5%85%B3%E9%94%AE%E8%B7%AF%E5%BE%84%E8%B6%85%E6%97%B6/" rel="prev" title="求关键路径超时">
                求关键路径超时 <i class="fa fa-chevron-right"></i>
              </a>
            
          </div>
        </div>
      

      
      
    </footer>
  </div>
  
  
  
  </article>



    <div class="post-spread">
      
    </div>
  </div>


          </div>
          


          

  



        </div>
        
          
  
  <div class="sidebar-toggle">
    <div class="sidebar-toggle-line-wrap">
      <span class="sidebar-toggle-line sidebar-toggle-line-first"></span>
      <span class="sidebar-toggle-line sidebar-toggle-line-middle"></span>
      <span class="sidebar-toggle-line sidebar-toggle-line-last"></span>
    </div>
  </div>

  <aside id="sidebar" class="sidebar">
    
    <div class="sidebar-inner">

      

      
        <ul class="sidebar-nav motion-element">
          <li class="sidebar-nav-toc sidebar-nav-active" data-target="post-toc-wrap">
            文章目录
          </li>
          <li class="sidebar-nav-overview" data-target="site-overview-wrap">
            站点概览
          </li>
        </ul>
      

      <section class="site-overview-wrap sidebar-panel">
        <div class="site-overview">
          <div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person">
            
              <p class="site-author-name" itemprop="name">羊书</p>
              <p class="site-description motion-element" itemprop="description">记录生活</p>
          </div>

          <nav class="site-state motion-element">

            
              <div class="site-state-item site-state-posts">
              
                <a href="/blog/archives/%7C%7Carchive">
              
                  <span class="site-state-item-count">8</span>
                  <span class="site-state-item-name">日志</span>
                </a>
              </div>
            

            
              
              
              <div class="site-state-item site-state-categories">
                <a href="/blog/categories/index.html">
                  <span class="site-state-item-count">1</span>
                  <span class="site-state-item-name">分类</span>
                </a>
              </div>
            

            
              
              
              <div class="site-state-item site-state-tags">
                <a href="/blog/tags/index.html">
                  <span class="site-state-item-count">16</span>
                  <span class="site-state-item-name">标签</span>
                </a>
              </div>
            

          </nav>

          

          
            <div class="links-of-author motion-element">
                
                  <span class="links-of-author-item">
                    <a href="https://github.com/yangshucheng1219" target="_blank" title="GitHub">
                      
                        <i class="fa fa-fw fa-github"></i>GitHub</a>
                  </span>
                
                  <span class="links-of-author-item">
                    <a href="mailto:ysc714@163.com" target="_blank" title="E-Mail">
                      
                        <i class="fa fa-fw fa-envelope"></i>E-Mail</a>
                  </span>
                
            </div>
          

          
          

          
          

          

        </div>
      </section>

      
      <!--noindex-->
        <section class="post-toc-wrap motion-element sidebar-panel sidebar-panel-active">
          <div class="post-toc">

            
              
            

            
              <div class="post-toc-content"><ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#数字组合等式问题"><span class="nav-number">1.</span> <span class="nav-text">数字组合等式问题</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#1-2-3-4-5-6-7-8-9-110"><span class="nav-number">1.1.</span> <span class="nav-text">1 2 3 4 5 6 7 8 9 &#x3D; 110</span></a></li></ol></li></ol></div>
            

          </div>
        </section>
      <!--/noindex-->
      

      

    </div>
  </aside>


        
      </div>
    </main>

    <footer id="footer" class="footer">
      <div class="footer-inner">
        <div class="copyright">&copy; <span itemprop="copyrightYear">2020</span>
  <span class="with-love">
    <i class="fa fa-user"></i>
  </span>
  <span class="author" itemprop="copyrightHolder">羊书</span>

  
</div>


  <div class="powered-by">由 <a class="theme-link" target="_blank" href="https://hexo.io">Hexo</a> 强力驱动</div>



  <span class="post-meta-divider">|</span>



  <div class="theme-info">主题 &mdash; <a class="theme-link" target="_blank" href="https://github.com/iissnan/hexo-theme-next">NexT.Muse</a> v5.1.4</div>




        







        
      </div>
    </footer>

    
      <div class="back-to-top">
        <i class="fa fa-arrow-up"></i>
        
      </div>
    

    

  </div>

  

<script type="text/javascript">
  if (Object.prototype.toString.call(window.Promise) !== '[object Function]') {
    window.Promise = null;
  }
</script>









  












  
  
    <script type="text/javascript" src="/blog/lib/jquery/index.js?v=2.1.3"></script>
  

  
  
    <script type="text/javascript" src="/blog/lib/fastclick/lib/fastclick.min.js?v=1.0.6"></script>
  

  
  
    <script type="text/javascript" src="/blog/lib/jquery_lazyload/jquery.lazyload.js?v=1.9.7"></script>
  

  
  
    <script type="text/javascript" src="/blog/lib/velocity/velocity.min.js?v=1.2.1"></script>
  

  
  
    <script type="text/javascript" src="/blog/lib/velocity/velocity.ui.min.js?v=1.2.1"></script>
  

  
  
    <script type="text/javascript" src="/blog/lib/fancybox/source/jquery.fancybox.pack.js?v=2.1.5"></script>
  


  


  <script type="text/javascript" src="/blog/js/src/utils.js?v=5.1.4"></script>

  <script type="text/javascript" src="/blog/js/src/motion.js?v=5.1.4"></script>



  
  

  
  <script type="text/javascript" src="/blog/js/src/scrollspy.js?v=5.1.4"></script>
<script type="text/javascript" src="/blog/js/src/post-details.js?v=5.1.4"></script>



  


  <script type="text/javascript" src="/blog/js/src/bootstrap.js?v=5.1.4"></script>



  


  




	





  





  












  





  

  

  

  
  

  

  

  

</body>
</html>
